There are two wires of same material. Their radii and lengths are both in the ratio 2 : 1. If the extensions produced are equal, what is the ratio of the loads ?

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2 : 1

1 : 2

1 : 4

4 : 1

answer is B.

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Detailed Solution

$y = \frac{F L}{A e} = \frac{F L}{π r^{2} e}$

$F = \frac{y π r^{2} e}{L}, F α \frac{r^{2}}{L} (∵ e a n d y a r e s a m e)$ , $\frac{F_{1}}{F_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} (\frac{L_{2}}{L_{1}})$

$= {(\frac{2}{1})}^{2} (\frac{1}{2}) = \frac{4}{2} = \frac{2}{1}$

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